There is a good reason for the pre-mailing... and it is not all about cost but about accuracy.
See, if you look at the mailer, you'll see that it includes a return service request.
This is something that is done by direct mail operations to prune the list
Pubby, this is in response to your statements above. (Mrs G, here)
The envelope we got with the "warning" letter (as someone called it) did NOT have any return service request. It just had the return address and that's all.